Introduction to Time - Varying Electrical Networks

Week 1:Motivation for the topics covered in the course, review of linearity and time-variance;Review of electrical network basics, incidence matrix, Tellegen's theorem;Tellegen's theorem (cntd), its use to prove reciprocity in bilateral networks, reciprocity in networks with controlled sources

Week 2:Reciprocity in networks with controlled sources (contd), inter-reciprocal networks;Modified Nodal Analysis (MNA) formulation to write network equations;MNA formulation (contd), MNA stamps of circuit elements, Reciprocity and inter-reciprocity revisited

Week 3:Reciprocity and inter-reciprocity (contd), the adjoint network.;Introduction to noise in electronic circuits;Noise in RLC circuits, Nyquist's theorem, Bode's Noise Theorem

Week 4:Bode's noise theorem (contd), input referred noise sources in networks;Input-referred noise sources (contd) - equivalent noise voltage and current sources;Equivalent noise sources, noise factor

Week 5:Need to study time-varying circuits and systems;Linear time-varying (LTV) system basics;Linear Periodically Time-Varying (LPTV) systems basics

Week 6:Harmonic transfer functions, the Zadeh expansion;MNA equations in LPTV networks with Harmonic transfer matrices;LPTV circuit example : the sampling mixer

Week 7:Impedance and admittance in LPTV networks, Norton and Thevenin equivalents;The N-path principle;N-path circuits (contd) - the time-interleaved ADC

Week 8:N-path circuits (contd) - the multiphase dc-dc converter, introduction to the N-path filter;N-path filters (contd) - input impedance and gain;N-path filters 

Week 9:Reciprocity and inter-reciprocity in LPTV networks - time-reversal to generate the adjoint;Inter-reciprocity (contd), transfer-function theorem;Inter-reciprocity (contd), the frequency-reversal theorem

Week 10:Inter-reciprocal signal-flow graphs. Example : chopped amplifiers;Chopped-amplifiers with sinusoidal and square-wave modulation;Adjoint networks - the switched-RC kernel example; time-domain implications of adjoint networks

Week 11:Time-domain implications of the adjoint - example of a switched-RC network. Sampled LPTV networks;Equivalent LTI filter of a sampled LPTV system; derivation of the equivalent impulse response, switched-RC network example ;Cont. time delta-sigma as a sampled LPTV system

Week 12:Response of LPTV systems to modulated inputs; equivalent LTI filter;Introduction to noise in LPTV networks, noise in switched-RLC networks, the Bode noise theorem applied to LPTV networks;Course summary and recap